Exponential inequalities for dependent V-statistics via random Fourier features

被引：6

作者：

Shen, Yandi ^{[1
]}

Han, Fang ^{[1
]}

Witten, Daniela ^{[1
]}

机构：

[1] Univ Washington, Seattle, WA 98195 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2020年 / 25卷

基金：

美国国家科学基金会;

关键词：

dependent V-statistics; strong mixing condition; kernel expansion; random Fourier features; U-STATISTICS; MOMENT INEQUALITIES; MISES STATISTICS; STATIONARY; DEGENERATE; BOOTSTRAP; SUMS;

D O I：

10.1214/20-EJP411

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We establish exponential inequalities for a class of V-statistics under strong mixing conditions. Our theory is developed via a novel kernel expansion based on random Fourier features and the use of a probabilistic method. This type of expansion is new and useful for handling many notorious classes of kernels.

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页数：18

相关论文

共 26 条

[1] Moment inequalities for U-statistics [J].

Adamczak, Radoslaw .

ANNALS OF PROBABILITY, 2006, 34 (06) :2288-2314

[2]

[Anonymous], CONCENTRATION INEQUA

[3] LIMIT-THEOREMS FOR U-PROCESSES [J].

ARCONES, MA ;

GINE, E .

ANNALS OF PROBABILITY, 1993, 21 (03) :1494-1542

[4] A martingale decomposition for quadratic forms of Markov chains (with applications) [J].

Atchade, Yves F. ;

Cattaneo, Matias D. .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2014, 124 (01) :646-677

[5] Deriving the asymptotic distribution of U- and V-statistics of dependent data using weighted empirical processes [J].

Beutner, Eric ;

Zaehle, Henryk .

BERNOULLI, 2012, 18 (03) :803-822

[6] A note on exponential inequalities for the distribution tails of canonical von Mises' statistics of dependent observations [J].

Borisov, I. S. ;

Volodko, N. V. .

STATISTICS & PROBABILITY LETTERS, 2015, 96 :287-291

[7] THE EMPIRICAL PROCESS OF SOME LONG-RANGE DEPENDENT SEQUENCES WITH AN APPLICATION TO U-STATISTICS [J].

DEHLING, H ;

TAQQU, MS .

ANNALS OF STATISTICS, 1989, 17 (04) :1767-1783

[8]

Dehling H., 2006, Lect. Notes Stat., V187, P65

[9] Central limit theorem and the bootstrap for U-statistics of strongly mixing data [J].

Dehling, Herold ;

Wendler, Martin .

JOURNAL OF MULTIVARIATE ANALYSIS, 2010, 101 (01) :126-137

[10] ON U-STATISTICS AND V MISES STATISTICS FOR WEAKLY DEPENDENT PROCESSES [J].

DENKER, M ;

KELLER, G .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1983, 64 (04) :505-522